Earlier quoted context omitted.
Linking conservation of energy is just non argument. It has nothing to do with anything, because our bodies are not simple theoretical machine.
They are still subject to the basic laws of physics. If you do a certain amount of work, but you take in less than what you have spent, the body has to use its stored energy to make up for the difference. How else would this work? The body cannot magically materialise energy out of nothing, and it cannot use more than what is available in the form of intake plus storage.
Your body temperature goes up and down, changing how much energy is spent by body. Your ability to perform goes up and down - you become sleepy and tired, your brain spends less energy and that is that (yes it has impact on your attention and performance). You cant stop it from happening. You may try to exercise the same and can easily become unable to.
Your body gets rid of calories in poo and piss, when sweating or not.
Your body can just turn off functions and generally malfunctions and you dont have direct control over it.